mlsanityData to 7 Oct 2026

Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Data

arXiv 2012.02334 ↗First posted 3 Dec 2020cs.LG cs.AI cs.SYcited by 40

Not on the map. Why?

Abstract (arXiv)

The last few years have witnessed an increased interest in incorporating physics-informed inductive bias in deep learning frameworks. In particular, a growing volume of literature has been exploring ways to enforce energy conservation while using neural networks for learning dynamics from observed time-series data. In this work, we survey ten recently proposed energy-conserving neural network models, including HNN, LNN, DeLaN, SymODEN, CHNN, CLNN and their variants. We provide a compact derivation of the theory behind these models and explain their similarities and differences. Their performance are compared in 4 physical systems. We point out the possibility of leveraging some of these energy-conserving models to design energy-based controllers.

Key facts. Cited by 40 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Dec 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 9; 2022: 18; 2023: 6; 2024: 2; 2025: 2; 2026: 3.

40 papers.

Sort:

By area:

  1. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  2. 2021Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modelingcited by 40
  3. 2021Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Modelscited by 33
  4. 2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
  5. 2021Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modelingcited by 27
  6. 2021Which priors matter? Benchmarking models for learning latent dynamicscited by 26
  7. 2022Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systemscited by 23
  8. 2022Learning Articulated Rigid Body Dynamics with Lagrangian Graph Neural Networkcited by 22
  9. 2022Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systemscited by 20
  10. 2022Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networkscited by 17
  11. 2022Physics-Informed Model-Based Reinforcement Learningcited by 17
  12. 2022Taylor-Lagrange Neural Ordinary Differential Equations: Toward Fast Training and Evaluation of Neural ODEscited by 13
28 more
  1. 2022Learning the Dynamics of Particle-based Systems with Lagrangian Graph Neural Networkscited by 11
  2. 2022Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systemscited by 11
  3. 2022Thermodynamics of learning physical phenomenacited by 10
  4. 2023How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equationscited by 10
  5. 2022Learning Neural Hamiltonian Dynamics: A Methodological Overviewcited by 8
  6. 2022Recognition Models to Learn Dynamics from Partial Observations with Neural ODEscited by 8
  7. 2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacousticcited by 7
  8. 2022Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systemscited by 7
  9. 2022Approximation of nearly-periodic symplectic maps via structure-preserving neural networkscited by 6
  10. 2021SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Visioncited by 5
  11. 2023Stability-Informed Initialization of Neural Ordinary Differential Equationscited by 5
  12. 2021Optimal Energy Shaping via Neural Approximatorscited by 4
  13. 2022Learning Trajectories of Hamiltonian Systems with Neural Networkscited by 4
  14. 2022ModLaNets: Learning Generalisable Dynamics via Modularity and Physical Inductive Biascited by 4
  15. 2021Lagrangian Neural Network with Differentiable Symmetries and Relational Inductive Biascited by 3
  16. 2023Discovering interpretable Lagrangian of dynamical systems from datacited by 3
  17. 2023Graph Neural Stochastic Differential Equations for Learning Brownian Dynamicscited by 2
  18. 2021Incorporating NODE with Pre-trained Neural Differential Operator for Learning Dynamicscited by 1
  19. 2022Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltoniancited by 1
  20. 2023Learning Latent Dynamics via Invariant Decomposition and (Spatio-)Temporal Transformerscited by 1
  21. 2023Discovering Symbolic Laws Directly from Trajectories with Hamiltonian Graph Neural Networkscited by 1
  22. 2024Lagrangian neural networks for nonholonomic mechanicscited by 1
  23. 2024Neural Port-Hamiltonian Differential Algebraic Equations for Compositional Learning of Electrical Networkscited by 1
  24. 2025Performance-Carbon Trade-Offs across Architectural Biases in Shear Flow Forecastingcited by 0
  25. 2025Physics-Informed Neural Controlled Differential Equations for Scalable Long Horizon Multi-Agent Motion Forecastingcited by 0
  26. 2026From Data to Laws: Neural Discovery of Conservation Laws Without False Positivescited by 0
  27. 2026Conservation Buys Stability and Factoring Buys Counterfactuals in Physical World Modelscited by 0
  28. 2026Stable and Counterfactually Robust Physical World Models from Imposed Structure and Learned Physicscited by 0